Abstract

We apply the method of Hamilton shooting to obtain the well-posedness of boundary value problems for certain Hamiltonian systems and
some estimates for their solutions. The examples of Hamiltonian functions
covered by the method include elliptic polynomials and exponentially growing
functions. As a consequence we prove global existence, smoothness and almost
everywhere uniqueness of absolute minimizers in the corresponding problem
of calculus of variations and hence construct the global field of extremals.